Certain clarifications on the resistive wall mode theorem and extensions

In a previous paper by V. D. Pustovitov [Phys. Plasmas 24, 112513 (2017)], it is claimed that the proofs of the Resistive-Wall-Mode theorem by Pfirsch and Tasso [Nucl. Fusion 11, 259 (1971)] and extensions of that theorem for time dependent wall resistivity and equilibrium plasma flow are not detailed and that there are limitations restricting their applicability. In response, we provide here pertinent detailed derivations, showing that the proofs of the above-mentioned theorems are rigorous and complete, unlike the considerations of V. D. Pustovitov [Phys. Plasmas 24, 112513 (2017)], which ignore the self-adjointness of the operator backward difference x backward difference x and the fact that the force operator in the linearized ideal MHD momentum equation remains self-adjoint in the presence of equilibrium flows.

Automated summary

This paper responds to a previous study by V. D. Pustovitov and provides detailed derivations of the proofs of the Resistive-Wall-Mode theorem by Pfirsch and Tasso, highlighting the overlooked issues of self-adjointness and the self-adjointness of the force operator.